Stochastic adaptation of importance sampler

Abstract

Improving efficiency of the importance sampler is at the centre of research on Monte Carlo methods. While the adaptive approach is usually not so straightforward within the Markov chain Monte Carlo framework, the counterpart in importance sampling can be justified and validated easily. We propose an iterative adaptation method for learning the proposal distribution of an importance sampler based on stochastic approximation. The stochastic approximation method can recruit general iterative optimization techniques like the minorization–maximization algorithm. The effectiveness of the approach in optimizing the Kullback divergence between the proposal distribution and the target is demonstrated using several examples.

Keywords:

• adaptive algorithm
• importance sampling
• stochastic approximation

Acknowledgements

We thank an anonymous reviewer and the associate editor for their helpful comments which greatly improved the manuscript. The research is funded by Singapore Ministry of Education Tier 1 Grant 36/09.